**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Sat, 9 Oct 1999 18:15:54 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 925] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"**Previous message:**Matti Pitkanen: "[time 923] Unitarity"**Next in thread:**Matti Pitkanen: "[time 925] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"

On Sat, 9 Oct 1999, Hitoshi Kitada wrote:

*> Dear Matti,
*

*>
*

*> Matti Pitkanen <matpitka@pcu.helsinki.fi> wrote:
*

*>
*

*> Subject: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your
*

*> proof of unitarity
*

*>
*

*> skip
*

*>
*

*> > > I am speaking of general context without such a condition. If the limit
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*> above
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*> > > exists, then it follows from it the unitarity.
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*> > >
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*> > You argue that you can avoid somehow the assumption about the
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*> > existence of the time development operator and get unitarity from
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*> > algebraic structure alone. Or that you have unitary time development
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*> > operator in case that you have only E=0 states
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*> > of Hamiltonian?
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*>
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*> This is not my argument, but it is an old theory of T. Kato and S. T. Kuroda:
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*>
*

I managed to modify purely formal unitarity proof by starting

from proof which I found from Merzbacher to apply to my case.

It is so horribly formal that it makes me sick(;-).

See the separate posting.

I however tend to believe to the condition V|m_1>=0 since it forces

p-adics and is consistent with the idea of renormalization group

invariance and leads to the cohomological interpretation.

The idea that S-matrix is so near to trivial one that one is forced

to go from reals to p-adics somehow satisfies my pathological mind

(I like dancing on the rope)(;-)-

*> Theory of simple scattering and eigenfunction expansions, Functional Analysis
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*> and Related Topics, Springer-Verlag, 1970, pp. 99-131,
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*>
*

I hope this is in the library.

*> and
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*>
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*> The abstract theory of scattering, Rocky Mount. J. Math., Vol. 1 (1971),
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*> 127-171.
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*>
*

*> I am not sure if your interaction term satisfies their assumptions. If it
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*> works with your case, their argument treats the Hamiltonian without assuming
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*> conditions like Virasoro conditions. They get a unitarity (completeness in
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*> their terminology) for general spectra. The spectral projection onto the space
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*> corresponding to E=0 would then give your unitarity.
*

I am afraid that I cannot judge whether these assumptions are satisfied.

In any case, it is interesting to look it.

*>
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*> The problem may be in the interaction term if their method does not work.
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*>
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*> A question related with this is if the E=0 states are genuine eigenvectors
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*> or generalized ones. Maybe to see if this is the case or not is included in
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*> your problem?
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*>
*

I am not sure what you mean with generalized eigenvector.

Best,

MP

**Next message:**Matti Pitkanen: "[time 925] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"**Previous message:**Matti Pitkanen: "[time 923] Unitarity"**Next in thread:**Matti Pitkanen: "[time 925] Re: [time 921] Re: [time 919] Re: [time 914] Re: [time 909] About your proof ofunitarity"

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